Parallel algorithms on circular-arc graphs

Abstract

Given a set of n circular arcs, the problem of finding a minimum cut has been considered in the sequential model. Here we present a parallel algorithm in the EREW-PRAM model that runs in O(log n) time with O( n) processors if the arcs are not given already sorted and using O( n log n ) processors otherwise. On the hypercube model, we consider the minimum cut as well as the following problems on a set of n circular-arcs: the minimum dominating set, the minimum circle cover, the maximum independent set, and the minimum clique cover. We give a parallel algorithm of time complexity O(log n log log n) and processor complexity O( n) for the minimum dominating set problem based on the hypercube model. For the minimum cut sequence, minimum circle cover, minimum clique cover, and maximum independent set problems, we give parallel algorithms of time complexity O(log n log log n + log m) and processor complexity O( n) if the input is not given sorted, otherwise, the time complexity is O(log n log m); m is the size of the solution set.